Hydrophobic models of protein folding and the thermodynamics of chain-boundary interactions

Abstract

We review some results concerning the energetic and dynamical consequences of taking a generic hydrophobic model of a random polypeptide chain, where the effective hydrophobic interactions are represented by Hookean springs. Then we present a set of calculations on a microscopic model of hydrophobic interactions, investigating the behaviour of a hydrophobic chain in the vicinity of a hydrophobic boundary. We conclude with some speculations as to the thermodynamics of pre-biotic functions proteins may have discharged very early on in the evolutionary past. I IntroductionThe approach of a statistical physicist to biological problems is different from that of a biologist, in the same way that the approach of a physicist to any natural phenomenon is different from that of an engineer. The difference seems to lie in regarding any given instance of a particular phenomenon not as the product of an ingenious design, but only as a member of a very large ensemble of possible realizations of a generic rule, all governed by the same laws of physics. To a statistical physicist, a biological molecule is not, first and foremost, a high precision tool custom-made to perform a highly specialized task; it is rather a member of a very large set of possible outcomes of random processes, which, under nonequilibrium conditions, have conspired to produce a certian, albeit very improbable result. Moreover, as has already been thoroughly underlined by Eigen [1] and Maynard-Smith [2], biological entities typically correspond to sharply peaked probability distributions ("quasispecies") about some point in biological phase space, rather than unique solutions to some optimization problem. This distribution is of course reflected in the genetic code, and also must translate itself to the proteins that make up the organism.Another source of deviations from perfect order is thermal noise. We would like to stress that the protein in its native state must essentially correspond to a self-organized system, i.e., the "native state" should be concieved of as the attractor of a dynamics [3]. This typically corresponds not to a unique conformation but to a set of conformations to which the trajectory of the phase point representing the molecule is confined after asymptotically long times (which may already be achieved in microseconds).In this paper we will first review a simple model involving discrete torsional degrees of freedom [3]. The hydrophobic interactions driving the folding of the polypeptide chain [4,5] are modeled by Hookean springs connecting pairs of hydrophobic residues. [6][7][8][9][10][11][12] This system, with harmonic interactions, under dissipative dynamics driven by random noise, leads to a distribution of energy states obeying a modified one-dimensional OrnsteinUhlenbeck [13,14] process, quite independently of the nature of the sequence of hydrophobic and polar residues, or the dimensionality of the space. It can be shown to obey the so called Wigner distribution [15][16][17][18][19] over a very large range of energies relative ...

Hydrophobic chains near hydrophobic surfaces—simulations in three dimensions

“…Apropos of the problem of protein folding, the picture we obtain is suggestive of a chaperoning function provided by the hydrophobic surface [20]. In fact, there exist studies which reveal that the chaperoning action of the protein 'chaperonin' can be simply modelled by the confinement of the protein inside a cylindrical cavity with hydrophobic walls [21].…”

Conformational gap and heat capacity peaks of short lattice polymers

“…As a result, we have the emergence of a peak in the heat capacity, since one needs to provide energy to break up non-covalent bonds and release the chain to access more degrees of freedom. Empirically, the hydrophobic effect, which several models mimic in their Hamiltonians [5], is viewed as the main driving force behind this process.…”